1. Field of the Invention
This invention relates to apparatus for monitoring and protecting ac electric power systems, and particularly to apparatus which provides an on-line measurement of frequency of waveforms in the ac electric power system.
2. Background Information
Frequency estimation is a very important function in power system protection. The frequency is not only an indication of power quality, but is also employed as a criterion for taking certain system control actions, such as load shedding. In addition, many protection functions and settings are based on the nominal frequency. In reality, power system frequency changes from time to time around the nominal value. Even through the variation from the nominal value is often very small, it may still make a significant difference in the frequency-related applications. For instance, the voltage and current phasors, which are essential to implement many metering and relay functions, are obtained based on the nominal power frequency through use of DFT (Discrete Fourier Transform). A deviation from the nominal frequency will result in errors in both magnitude and phase of the phasor, and in turn, these errors will migrate into metering and relaying functions. If an accurate frequency estimation could be obtained, these errors would be minimized or eliminated.
The most popular methods for frequency measurement available today are the zero-crossing and DFT based techniques. As is well known, the accuracy of the zero-crossing method is influenced by harmonics but can be improved by using the least square technique or other noise-suppressing techniques. On the other hand in the DFT based method, whether based on the magnitude or phase angle of a phasor, if all three-phase voltages are not available, the estimated frequency will be oscillatory when the system frequency deviates from the nominal frequency. This oscillatory frequency is double the system frequency. The envelope of the estimated frequency increases with increasing deviation from the nominal frequency. Usually, the oscillatory frequency is smoothed through use of an average filter. However, with such a filter, the estimated frequency becomes stationary only at certain system frequencies while remaining oscillatory for other deviant system frequencies. It can be shown that with an average filter, the envelope of the estimated frequency will be a standing wave of increasing amplitude as the deviation from the nominal frequency increases. The standing points are dependent on the length of the average filter used. For instance, a two-cycle filter will result in three standing points at which the system frequencies are multiples of one-fourth the nominal frequency. This means that the estimation accuracy is system frequency dependent. An accurate frequency is only obtained at the standing points. An accurate estimation over a wide range of frequencies may be achieved by using adaptive approaches. These include the adaptive sampling period, the adaptive length of the data window and adaptive filtering. Unfortunately, all of the adaptive approaches involve a considerable amount of computation in order to achieve better results.
There is a need therefore, for improved apparatus for determining the frequency in an ac electric power system.
There is a further need for such apparatus, which provides such an estimation of frequency with a consistent and predictable accuracy.
There is also a need for such apparatus which does not require excessive calculation, and can therefore, provide an accurate estimation of frequency on-line with a reasonable computational burden and cost.
These needs and others are satisfied by the invention which is directed to apparatus for providing an accurate on-line indication of frequency in an ac electric power system. The apparatus utilizes a time domain approach and includes processing a sensed waveform in the electric power system to generate what I have identified as a double average. This double average is derived from a few consecutive samples of the waveforn. More particularly, the double average signal is the sum of a most recent value of the waveform, twice the next most recent value of the waveform and the third most recent value of the waveforn. Means process this double average signal to generate a frequency signal. This frequency signal can be used in an analyzer or protective device such as a protective relay or a circuit breaker which interrupts the current in the electrical system. This basic system generates an indeterminate frequency when the next most recent sample has a zero value, i.e. at a zero crossing. Also the accuracy of this basic system is reduced by noise.
To further improve the accuracy of the apparatus, additional means generating a running average of the double average signal is used. Preferably, this additional means provides a least square value of the double average signal, although other noise suppression techniques such as a straight average can also be used.
Preferably, the apparatus includes a digital processor in which case sensing means generates digital samples of the selected waveform in the ac electric power system. The three most recent digital samples are utilized to calculate the current value of the digital double average signal, which is then used by means in the digital processor to generate a digital frequency signal. In protection apparatus such as a protective relay or circuit breaker, the digital frequency signal is compared to limits and means are provided which interrupt current in the electric power system in the event that the digital frequency signal is outside the limits. Again, the digital system includes means for generating a running digital double average signal in a sliding window of time. This running digital double average signal can be implemented by means of applying a least mean square function or a straight average function to a selected number of the most recent digital double average signals.
Therefore, it is an object of the invention to provide improved apparatus for determining the frequency in an ac electric power system. It is a further object of the invention to provide such apparatus which determines the frequency with consistent accuracy without excessive calculations and can do so on-line.